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A circle is inscribed in a square as shown - Leaving Cert Mathematics - Question 1 - 2010

Question 1

A circle is inscribed in a square as shown. The radius of the circle is 9 cm. (i) Find the perimeter of the square. (ii) Calculate the area of the square.

Worked Solution & Example Answer:A circle is inscribed in a square as shown - Leaving Cert Mathematics - Question 1 - 2010

Step 1

(i) Find the perimeter of the square.

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Answer

To find the perimeter of the square, we first note that the radius of the inscribed circle is equal to half the length of the side of the square. Since the radius is 9 cm, the side length (l) of the square can be calculated as:

$l = 2 \times 9 = 18 \text{ cm}$

The perimeter (P) of the square is then given by the formula:

$P = 4l = 4 \times 18 = 72 \text{ cm}$

Step 2

(ii) Calculate the area of the square.

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Answer

The area (A) of the square can be calculated using the formula:

$A = l^2$

Substituting the side length:

$A = (18)^2 = 324 \text{ cm}^2$

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